Answer
$\frac{25}{6}$ meters
Work Step by Step
Step 1: Since the triangles are similar, their corresponding sides are in
proportion.
Step 2: This means that $\frac{12}{5}=\frac{10}{y}$.
Step 3: Solving through cross multiplication: $12y=5\times10$.
Step 4: $12y=50$
Step 5: $y=\frac{50}{12}=\frac{25}{6}$ meters.
Check:
Step 1: Equating the two proportions to see if they reduce to the same fraction: $\frac{12}{5}=\frac{10}{\frac{25}{6}}$
Step 2: Simplifying both sides, $\frac{12}{5}=\frac{10\times6}{25}$
Step 3: $\frac{12}{5}=\frac{60}{25}$
Step 4: $\frac{12}{5}=\frac{12}{5}$
Step 5: Therefore, the answer is accurate.